Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the peria nkdtd7me *8,odic table or Appendix tnka*edmd8, 7 B.

Name several properties of materials that could be exploited to make a thermomeexmw8s8 c: c0ttet xcm0:88csw er.

Which is larger, 1 C a )kv8r;nj- r5oj(zlh$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium ckjma:z2,s6iy4f 3i)8mih qbwith system B, but B is not in thermal equilibrium with system C, what can you say about the temperatures ohkafm ,8:miqs)24ciby6izj 3 f A, B, and C?

A flat bimetallic strip co di5g-wz kknw-)i-ypjb/; :fgnsists of aluminum riveted to a strip of iron. When heated, the strip will bend. Which metal will be on the outside of the curve? [Hint: See Table/5ik:wnz gi- pd ywg)fj-bk-; 13–1.] Why?

In the relation $\Delta$L = $\alpha$ $L_0$ $\Delta$T, should $L_0$ be the initial length, the final length, or does it matter? Explain.

The units for the coefficient of fl8s+ l0zsv:c 5n 3wwlq*y 5gxlinear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a dia:wa: n5j;tunlpih5n2 08dh d egram of a simple thermostat used to control a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricityn5ehl:;hdn 0 a8in:2twd5jp u when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at tbu0- go9uzmu a5mxq 08he ends often have a section in the shape of a U.-mgob85 0a9qzum u0 ux Why?

A flat, uniform cylinder of lead fl lfuj11*lpo qfxu95ol dsf+-zk - p-0moats in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first placed in a hot tub of watn(iera kergdq9k u,bq: ,f9+8er, the mercury initially descends a bit and then rifnr e+,k:kg 8(99drua bq,qei ses. Explain.

A glass container may*5mwct 2 q(7sl+yi9szf eajn. break if one part of it is heated or cooled more rapidly than adjacena5wjzs(.2+7mt*if sel cn qy9t parts. Explain.

The principal virtue of Pyrex glass is that its coeffog)z5y(3 oxa+eies 6 zicient of linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this gives rise tzx(es y e)zoo6+i5 ag3o the increased heat resistance of Pyrex.

Will a grandfather clock, accurate at 20rkdv ;g- 5)b8j)f 4r3q otppsq $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of so4lnc+mz+x.3zjv : do *oe3vyo da will cause its bottom and top to bulge so badly the can will not stand up. What has happendvoc mzo*.+3yl 4nov j: z3e+xed?

When a gas is rapidly compressed (xtbo h6e9jn2:say, by pushing down a piston), its temperature ixen9th2 o:6jbncreases. When a gas expands against a piston, it cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminum sphere submerged in watsj;; m+mv5vcs er increase or decrease if the temperature vj;sc vsm;m+5 is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetihtxtx-8n8r tzb0 3c3xy1gta ,c theory and the relation between ya3xthr tn- tg,x 8cbz80x31taverage kinetic energy and the absolute temperature.

Explain in words how Gay-Lussac’s law follows from kineti a do( vr9-e0ku7jmfx:c theory.

As you go higher in the Earthq,/e hvis 8ku 9dnbx7;’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimum speed an objelbu 5v e+ mheci(5yvxusu.(;+ct must have to leave the Earth and never return. The 5h(v+me su ;ui.eu+cvb5(xyl escape velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickly than water at room temperwc/; l1eu,bjt of6q6n7 glk)rature. What can you infer about the motl1/7 flk)qr,u; g6b6wn ecjolecular properties of one relative to the other?

Explain why a hot humid day is far more uncomfortable than *bd0l npsprys 6t)jm sm58,i0a hot dry day at the same jpp0n, st6yrb )m 0l*5sdms8 itemperature.

Is it possible to boil water at room temperatt(3wno.erns be58( na ure (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature iu+pma+ygc 6c5ap r-2 ns the same but the humidity is different. Which is more dense, the dry air or the hc6p-rc m pga+a u2n+y5umid air at the same T? Explain.

Explain why it is dangerous to open *w2o9hr:k*nctx ak-pthe radiator cap of an overheated automobile eng nrc9x:o*-phtw * k2akine.

Why does exhaled air appearqv4cae(kb-/wrs; nz0 as a little white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.4i 2jay)yd099bvpcmo d ;h.c 7thr/dm k*3 toz)-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring gfw 2ud c4844bgkst;k compare to the number in a silver ring of the same g284wsc;t d4fkk gub4mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be x ut) qj(7hfj368°F. What is this on the Celsius scale?hj3xq)u(t jf 7   $^{\circ} $ C
(b) The temperature of the filament in a lightbulb is about 1800 $^{\circ} $ C. What is this on the Fahrenheit scale?    $^{\circ} $ F

  Among the highest and lowest 0 ,zp*kp4 9gm0g8rylxiz6 ykzg(b2t hw :ax2rtemperatures recorded are 136 $^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

  (a) 15 $^{\circ} $ below zero on the Celsius scale is what Fahrenheit temperature?    $^{\circ} $ F
(b) 15 $^{\circ} $ below zero on the Fahrenheit scale is what Celsius temperature?   $^{\circ} $ C

  In an alcohol-in-glass thermometer, the alcohol column has lenglm.1 muib 5 nl785xhaw ,uw1gbth 11.82 cm at 0.0 8u7abgbw xm15 wull. i51mnh ,$^{\circ} $ C and length 22.85 cm at 100.0 $^{\circ} $ C. What is the temperature if the column has length
(a) 16.70 cm,    $^{\circ} $ C
(b) 20.50 cm?    $^{\circ} $ C

  A concrete highway is built of slabs 12 m long :)j1r /7pumwwk5 kv dh(20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

  Super Inva$^{TM}$, an alloy of iron and nickel, is a strong material with a very low coefficient of linear expansion [0.2$ \times10^{ -6}$(C?)$^{-1}$]
A 2.0-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this table expand along its length if the temperature increases 5.0 $^{\circ} $ C? Compare to tabletops made of steel.   $ \times10^{-6 }$ m    $ \times10^{-4 }$ m

  The Eiffel Tower (Fig. 13–29) is built of wrought iron approximately 300 v;e5h5z )leoe m tall. Estimate how much its height changes between July (average temperature of z;h 5v)e5oeel25°C) and January (average temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger than the rivet hole are often un f d.bfqr l yuxfwv9 6*7v4s 3h9ro2v,t.y-oosed and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed , f6*y9 y4d .qh3t ls-2xbrwvrfu f9ovo7vn.oin a hole 1.869 cm in diameter at 20 $^{\circ} $ C. To what temperature must the rivet be cooled if it is to fit in the hole?    $^{\circ} $ C

  The density of water+2 jl9fpsua7uniwq +q 6g+lb2 at 4 $^{\circ} $ C is $ 1\times10^{3 }kg/m^3$ What is water’s density at 94 $^{\circ} $ C?    kg/$m^3$

  A quartz sphere is 8.75 cm in diameter. What will be its ch j5i/. +biglhuange in volume if it is helh./u5biig+ jated from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the by ph9y)l( r ,7cerlh21 ihp3nkrim with 350.0 mL of water at 100.0$^{\circ} $ C. If the temperature decreased to 20.0 $^{\circ} $ C, how much water could be added to the glass?    mL

  It is observed that 55.50 mL ot r skj4yu3/ mq38l 7otytx*r.f water at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be plact fz e35tus8u0ed in a ring made of iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contained in a long, narrow vessel so itvjbsp4uw0o 79 can expand in essentially one direction only, show that the effective coefficient 7j4 uop9w0 svbof linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in the d+ie7x8)kgms .grc o*censity $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate of length l and width w has coefficient of 7x.zu95q mycglinear expa9c5g7mxqz uy. nsion $\alpha$ Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change $\Delta$T is $\Delta$A = 2$\alpha l w$$\Delta$T See Fig. 13–30.

Show that for an isotropic solilvq*a/gq v;1l d, $\beta$ = 3$\alpha$ if the amount of expansion is small. $\beta$ and $\alpha$ are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.]

  The pendulum in a grandfather clock is made of brass and keeps perfect time at ugxcj5bk xf; j 429ea917 a29bjfje95kx cg;x u4 $^{\circ} $ C. How much time is gained or lost in a year if the clock is kept at 25 $^{\circ} $ C? (Assume the frequency dependence on length for a simple pendulum applies.)$\approx$    min(Round to the nearest integer)

  (a) The tube of a mercury thermometer has an inside diameter of 0.140 mm. The .wml-q7alf qrh b,dztr15:r4bulb has a volume ozq5tm-1:rwrbq , 74lrlfd. haf 0.255 $cm^3$ How far will the thread of mercury move when the temperature changes from 11.5 $^{\circ} $ C to 33.0 $^{\circ} $ C? Take into account expansion of the Pyrex glass.    cm(b) Determine a formula for the length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

  A 23.4-kg solid aluminum cylindrical wheel of radius 7rtxbh,:oy+b *eg1/l o)efju 0.41 m is rotating about its axle on frictionless bearings with angular veloci t+ x) jlguof:1rbeh *,/yoeb7ty $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desiws1mcbo p;z;5xr ))8 rbztn.dred length when at 15°C. How much stress is required to keep it at this length if tx5csm;d1z )b rp. wn b;r8to)zhe temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectional ar z7 /,bec qo gt7pa (efvan4v6(j2s.sgea 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diametertqc//twor :v zlw r.nnr:;.x9 134.122 cm at 20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following temwt q ae6w/ b/(h1s zoc,eh)y(3le5rb cperatures on the Kelvin scale:
(a) 86$^{\circ} $ C,    K
(b) 78$^{\circ} $F,    K
(c) -100$^{\circ} $C    K
(d) 5500°C,    K
(e) -459$^{\circ} $F    K

  Absolute zero is what temperaturef x4lt8bi +bkxcf3 8jd(+ d0gj on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Skn** c)rho,m fun are about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

  If 3 $m^2$ of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0$^{\circ} $ C. What is the volume?    $m^3$

  In an internal combustion engine, air at atmospheric pr+kk6e;ppw 7or ko+/;bjuw:d sessure and a temperature of abo 7 pu+sw;rk ob;w:kdepjok+/6ut 20$^{\circ} $C is compressed in the cylinder by a piston to $\frac{1}{9}$ of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.    $^{\circ} $ C

  Calculate the density of oxygen at S:0wvy(:r.b -(ioca jzxnl; aeTP using the ideal gas law.    kg/$m^3$

  A storage tank contain8qceg1 c +*yv3o2y tnus 21.6 kg of nitrogen ($N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP contains 18.5 kg o+t 4qj n3m)oq.m 1m-z6qyxybsf nitrogen ($N_2$)
(a) What is the volume of the tank? $\approx$   $m^3$(“Round to one decimal places)
(b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?    $ \times10^{5 }$Pa    atm

  If 18.75 mol of helium gas tc1 osi/n0r +fis at 10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure inside a 35.0-L con 8b-e- mzomt:(;pkf h ,:wrov 78wuxsytainer holding 105.0 kg of argon gas at 38 ptbvf 8m-;-kms( yzxo7: oue w:hw,r85 K?   $ \times10^{ 8}$Pa

  A tank contains 26.0qzqvx rs2v1(q)x a+a6our4pn/wu; /y kg of $O_2$ gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?    kg He

  A hot-air balloon achieves its buoyant lift by heating the air inside the ballooygy9eu/9mxbcvvsc 97 ; ;vjo; n, which makes it less dense than the air outside. Suppose tvcev uxsj9o; ;bg9m7yc;9y /vhe volume of a balloon is 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled withr9 p 4)ts qm/xny:cz/m air at 15 $^{\circ} $ C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38 $^{\circ} $ C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?    %

  If 61.5 L of oxygen at 1ryqgl v06j j73ul4z1w4+ef on 8.0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloosy1qmbu ,nx; ;h /gb1pn escapes a child’s hand at sea level and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of molecutr;mz gzu:8 5 .nx3hdtles / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.hz; - wr5y. /ke1lwaxa000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number ofs y9tq9a6 i.e;iy 1lls (a) moles,    $ \times10^{22 }$ moles and (b) molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 km. $\approx$    $ \times10^{46 }$ molecules

  A cubic box of volume 6/ewk e if8ew:5.1$ \times10^{ -2}m^3$ is filled with air at atmospheric pressure at 20 $^{\circ} $ C. The box is closed and heated to 180 $^{\circ} $ C. What is the net force on each side of the box?    N

  Estimate how many molecules of a /in.lv:s+qvb ir are in each 2.0-L breath you inhale that were also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high a:n lv. bisq/v+nd of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy oflbw5 t*6gp;jgig+ r2r an oxygen molecule at STP tjr;g2 g*rip5+l6bgw?    $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of helium atoms near the surface of the Sun at a te0e wrk/) e;fpbf :x*nlpkg79xmperatu7;lp:p)rk wxge e/n *xkfb0f9re of about 6000 K.    m/s

  By what factor will the rms speed of gas mole jlkm1qte.(s9cules increase if the temperature is incre9lq t(se jm1k.ased from 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

  A gas is at 20 $^{\circ} $ C. To what temperature must it be raised to double the rms speed of its molecules?    $^{\circ} $ C

  Twelve molecules have the following speeds, given in units of km/s: v9obd7g3q) eu6, 2, 4, 6, 0, 4, 1, 8g 7bv) e93qodu, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in q*3 e(n, tg7no b; fripbv0 7ifnjhz7.a gas at 20.0 $^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doisdda6:k9 r :g/j yi. :cqszx6ubled while its volume is held constant, by what factor doesq6c9s :/g x6drdkias: :z j.yi $v_{rms}$ change?   

Show that the rms speed of molecules in a gas is givenhi*y g :m6vs x,08noxm--ju:nkvyq d9 by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of two gases an ,6jit7:iij mt the same temperature, the ratio of their rms speeds is equal to the inverse ratio of jti 76 jin,m:ithe square roots of their molecular masses.

  What is the rms speed oq93 gij -+ ixt77gedqsf nitrogen molecules contained in an 8.5$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed o1k3beea tz ddftuzn/+d,ka54 f0wp 5;f an oxygen molecule at 0 $^{\circ} $ C    m/s
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.    round trips per sec

  What is the average distance between nitrogen mol+(.tsajug(g yu 08 mppecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecular mass is 8s s,zv)p+bg++jj 6oee4+o zhb9 u in a livis6h zb+4 opg,sj oje)vb+e+z+ng cell at 37 $^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of(8pl7g0vhr r3xogc0il 6 d se;:in3na a gas can be written P = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of uranium, y-kr q3yc*n3m5 jx,lc$^{235}$U and $^{238}$U (the superscripts refer to their atomic mass), can be separated by a gas-diffusion process by combining them with fluorine to make the gaseous compound UF$_6$ Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T.   

(a) At atmospheric pressue/3qa a4 uzfw3re, in what phases can $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressure is 0.01 atm and the temperature iild/7n-y.u1ynoo9 pos (a) yoiod/1nyp .-9u7lo n90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a ds 2*u:u5nb eh+ol w8bgxl tp7+ay when the tempera+5w2 gl ext8nu7* pb :ulh+bosture is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure83g)umy xmd+ baywn3o v/69ht9)ewacr5w9pc at a place where water boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a parb, vv )vh4obyhy; :vr,kkss,5ticular place in the mountains is 0.72 atm, estimate b,,s o)4rhvvyk;hy bvsk5:v,the temperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water m+sna0ox /: qsis 530 Pa and the relative humidity is na q/0:s xos+m40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day ww8 c r5lvctmr)i65)d9o+zr53dak eughen the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pres+nxt0 s(f*f(*l qjv(ondhm / vv)q:cj sure inside a pressure cooker if the water is boiling at /0q sxfv(v(nhm l+:tc*qn* (dvo)jjfa temperature of 120 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a room of volumrzx(f jlqi6ax+7)rpy2pc(2j e 680$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew point of 59dnd58exrebfm ) a(j; u b4fl- $^{\circ} $ C is drawn into a building where it is heated to 25. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.    %

  Estimate the time needed fop5-7la+)dz-dg/ow8hm b9 g0v if j ol7ix7tgsr a glycine molecule (see Table 13–4) to diffuse a distance of h 7gj8do g7f ts vigo-5pd /-0awz+ l)lb9xi7m15 $\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from the surface of insects to the interior through tiny tu438oe sdns k+. 4psvqebes called tracheae. An average trachea is about 2 mm long ap q3oedsk4s8.+s v4nend has cross-sectional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure ha7l x)1 ehee4bts been calibrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A precise steel tape measure has been calibratel pty- 7f6ow v;rt(gin/; r(jgd at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A Pyrex measuring cup was calibrated at normal room temperature. How much err z5xiww-6pxrxiuflwo46 m218or will be made in a recipe calling for 300 mL of cool wa8wx w lipur26z-4m i5x 6oxwf1ter, if the water and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylindg5*n/l l .czolq,8fv:k y 5m0evrcc a8er is initially 28 atm. After many balloonsco,0 v5 ln58/ f mgv8*c.rc akzyelq:l have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?   

  Estimate the number of air molecules in a room of length 6.5 m, width 3.1 m, 2yxfs-/ezy1ylu .( m whmc- /pand height 2.5 m. Assume the temperatu p1 (ex lyyw//hmfsz m.-c2u-yre is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the d443oibcviy7 mk :jaq.z)ci -kensity of matter is about one atom per $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attainaa thmp*+:t6ncu +mj0u ble using the best available vacuum techniques is abouttm:0npma h++tc u *u6j $10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver fills his lungs to full capacity of 5.5 L when 10 mnwd9*f i8*q txgc o;9wt mu6mtc kl/84 below the surface, to what volume would his lungs expand ifx8/cft8tl69*n* ti w 9mwu ;4d gokmqc he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from tp+sx/8wwgs00 52c3hu vb2t 7r w fflemhe Moon enters Earth’s atmosphere at a speed of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize/w+2mtr 5bxcw30h g fuw 2fp8elv7ss0, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gaspdzc9:f/kj3(j,jx- lqc1kex96ilrl is increased from 110$^{\circ} $C to 360$^{\circ} $C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does $v_{rms}$ change?$\frac{P_2}{P_1}$ =    $\frac{(v_{rms})_2}{(v_{rms})_1}$ =   

  A house has a volume of q7cupobl w/c858 0ugs770m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pr) 6m ri 1ci6nh/zys t36f2j4ru7 aflufessure at the surface of the Earth, estimate the total number of air molecules in the Earth’i /)uhrfzt uj4r16s fyam3 lni 62f76cs atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of*pra w1- ybw gq9krt0+v7 w(nhm 6e;dy nitrogen molecules contained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of oxygen used in a hospital has gauge pressure = 2000rs*8;vei8b dx;b 50) bldmj uwkeea+* psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 w l * +x)e;jb;adbi0kr8d5eb*suev8mL/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury hb5a lhb64f)e3 u ezr.at 0$^{\circ} $C. (a) If the temperature is raised to 25$^{\circ} $C, will the cube float higher or lower in the mercury? ----待选择----lowerheigher 
(b) By what percent will the fraction of volume submerged change?    %

  The density of gasoline at i7gkh *c3mx9(vyt 6un 0$^{\circ} $C is 0.68$ \times10^{3 }kg/m^3$ What is the density on a hot day, when the temperature is 38$^{\circ} $C?    kg/$m^3$
What is the percentage change?    %

  If a steel band were to fit snugly around the Earth’s equator at 2w7 *g,h:1n beudk tw3e5$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws tightly onto a glaai7e rb5ut1 g ofw(;4jss jar at 20$^{\circ} $C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60$^{\circ} $C. The inside diameter of the lid is 8.0 cm at 20$^{\circ} $C. Find the size of the gap (difference in radius) that develops by this procedure.    cm

  The first length standard, adopted igj-a0g jv xo/,n the 18$^{th}$ century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within $\pm1.0 \mu m$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is $ 9\times10^{ -6}C/^{-1}$. $\pm$ =    C$^{\circ} $

  A scuba tank, when fully charged, has a pres/pge7 w3huv+0t k,vcz sure of 195 atm at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed from the)t.y cevn+bc )te,.pq0vat 9h Earth is $ 1.12\times10^{4 } m/s$ so a gas molecule travelling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field. At what temperature is the average speed of
(a) oxygen molecules,    $ \times10^{5 }$K
(b) helium atoms equal to $ 1.12\times10^{4 } m/s$    $ \times10^{4}$K
(c) Can you see why our atmosphere contains oxygen but not helium?

  A 1.0-kg trash-can lid is suspended awk1 h.n ewx:a6gainst gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elasticallhwxk :ne.w1a 6y, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (spherical) bcpxx4p jf(zf+ i9b3 q(c3 me4hubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gas.4i+ffjeh3m(q9x b(p4czx p c3 How large is the bubble when it reaches the surface?    cm

  Calculate the total water vapor pressure in the f9oxsg p9vb lk8si/yta 715/wair on the following two days: 5s1t/ygki/9 osv7l8p b9fxa w
(a) a hot summer day, with the temperature 30$^{\circ} $C and the relative humidity at 40%;    Pa
(b) a cold winter day, with the temperature 5$^{\circ} $C and the relative humidity at 80%.    Pa

  A sauna has 7$m^3$ of air volume, and the temperature is 90$^{\circ} $C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3.)    kg

  Estimate the percent difference in the density of iron at STP, and when it iu3 h.qp/g 5 jkagxzc*sosf776 s a solid deep/.chsjux k73g*p 7osga zq65 f in the Earth where the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to savtithl* aa/h4 uqq) al)hs4y4(qy,2 how that, for an ideal gas at constant pressure, the coefficient of volume expansion 4)ahq2la vyly/qth4h *,aa)qstiu 4(is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people constantly dehumidify their cellars o:8n-nb8v shg:tc /a (()ppnnj;ych rto prevent rot and yn (:hc/grph ;-:n avjb8o)sc 8( nptnmildew. If the cellar in a house (kept at 20$^{\circ} $C) has 95 $m^2$ of floor space and a ceiling height of 2.8 m, what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30%?    kg